Size Effect on Phase Transition

A simple model without adjustable parameters for size-dependent melting temperature of nanocrystals has been determined in terms of the size-dependent amplitude of the atomic thermal vibrations of nanocrystals according to Lindemann′s criterion on melting. The model predicts not only melting temperature depression for free-standing nanocrystals but also the melting temperature elevation for embedded nanocrystals in a matrix. The above model can be extended to predict the size dependence of the melting enthalpy and the cohesive energy of nanocrystals, the critical temperature for surface melting, the critical temperature for glass transition of polymers, and the critical temperatures of ferromagnetic, ferroelectric, and superconductor nanocrystals. It is found that the model predictions are in good agreement with the available experimental results.